Stabilizing and manipulating exotic emergent quasiparticles is one of the main goal of modern condensed matter physics. The quest for observing Majorana fermions and their non-Abelian braiding statistics in superconducting nanostructures is currently attracting a lot of attention, with fascinating prospects in fault-tolerant quantum computation. Parafermions are the simplest generalization of Majorana fermions: they show non-Abelian fractional statistics and are typically associated with topological phases. We will discuss the possibility of harboring these exotic excitations in genuinely one-dimensional electronic platforms. We focus on a specific model of fermions in one dimension with a generalized ZN multiplet pairing extending the standard and so-called Kitaev chain model. Using a combination of analytical techniques, we find an interesting topological phase intertwined with spontaneous symmetry breaking. Each symmetry-breaking sector is shown to possess a pair of boundary Majorana fermions encoding a topological character. A careful study of the quantum anomaly through pumping in the system finally reveals that parafermions exist in one dimension but only as non-local operators.
References:
Fernando Iemini, Christophe Mora & Leonardo Mazza, Topological phases of parafermions: a model with exactly-solvable ground states, Phys. Rev. Lett. 118, 170402 (2017)
Leonardo Mazza, Fernando Iemini, Marcello Dalmonte & Christophe Mora, Poor man’s parafermions in a lattice model with even multiplet pairing, preprint cond-mat arXiv:1801.08548.